In a 30-60-90 triangle, the lengths of the sides are in a specific ratio:
- The side opposite the 30-degree angle (shortest side) is \( x \).
- The side opposite the 60-degree angle (longer leg) is \( x\sqrt{3} \).
- The side opposite the 90-degree angle (hypotenuse) is \( 2x \).
Given that the side opposite the 60-degree angle is \( 6\sqrt{3} \), we can set up the equation:
\[ x\sqrt{3} = 6\sqrt{3} \]
To find \( x \), we divide both sides by \( \sqrt{3} \):
\[ x = 6 \]
Now, we can find the length of the hypotenuse, which is \( 2x \):
\[ \text{Hypotenuse} = 2x = 2(6) = 12 \]
Therefore, the length of the hypotenuse is 12.